The female squats over the male on his back taking him anally, riding until completion. The female can be facing in either direction, thus there is no diferentiation between a brown cowgirl and a reverse brown cowgirl - if a girl is squatting with your cock up her ass, its pretty much just all brown cowgirl.

You are right about her, not only does she take it up the ass but she wants it that way - five minutes on the couch and she was riding me brown cowgirl.